In dynamical systems, at least one property of the system varies with time in response to external disturbances. Examples include acoustical systems where the fluid pressure or velocity varies, mechanical systems where stresses or displacement varies, electrical system where the voltage or current varies and optical systems where the intensity of light varies. The analysis of dynamical systems is important in a great many areas, including monitoring, testing and control. There are usually two primary objectives (1) characterization of the dynamic disturbance of the system and (2) characterization of a dynamic response model which predicts how the system will respond to external disturbances. For example, in a control system, the disturbance must be characterized to determine if control action is required and the dynamic response model must be known in order to determine the appropriate control signal to apply.
Disturbance Characterization
Disturbances can be classified as being either broadband or narrowband. An example of broadband noise is wind noise heard in an automobile cabin. Examples of narrowband noise include the hum produced by a power transformer or the repetitive vibration of a rotating machine. Stationary, broadband signals, such as that which results from a recording of the noise from an air-conditioning vent, are usually characterized mathematically by a power spectrum, such as obtained by a third-octave spectral analysis, while transient broadband signals, such as impacts, may be characterized by time-frequency analysis, such as the short-term Fourier transform and the spectrogram or a wavelet transform.
This invention relates to the analysis of transient, broadband and narrowband disturbances.
Narrowband disturbances are so called because the majority of the power in the disturbance is concentrated in narrow frequency bands. The position of the frequency bands is determined by the external source of the disturbance and can therefore change when the source changes. Narrowband disturbances are often characterized by order analysis. In order analysis, the power of the disturbance in each of the narrow frequency bands is estimated, this contrasts to Fourier analysis in which the frequency bands are fixed and are not related to the source. Order analysis is used in many areas, for example: noise and vibration analysis, condition based monitoring of rotating machines, active noise and vibration control, higher harmonic control, machinery balancing and alignment. Order analysis systems typically use a synchronization signal. The analysis is performed either by a bank of tracking filters, which separate the signal into narrow frequency bands and then compute the power in each band, or by synchronous sampling in which the sampling rate is varied so that the frequencies of a discrete Fourier transform coincide with the frequencies of the source. Tracking filters have a major disadvantage in that there is a fundamental trade-off between the bandwidth of the filter (which should be narrow to reject noise and nearby tonal components) and the ability to track changing signals (which requires a broader filter to reduce delay). An example of such a system is shown in FIG. 1. A sensor 2 is used to sense the disturbance of a dynamic system 1 and produce a signal 3. A synchronizing signal 100, derived from a tachometer for example, is indicative of the frequency or phase of the system. The synchronizing signal is passed to tone generators 101, 101', 101" which each generate complex (in-phase and quadrature) signals at one of the harmonics of the fundamental frequency of the disturbance. The signal 3 is multiplied at 102, 102', 102" by each of the complex signals and passed through low pass filters 103, 103', 103" (which may be integrators) to produce estimates of the complex amplitudes at each harmonic frequency, as indicated 104, 104', 104". These estimated signals provide an indication of the amplitude of the disturbance at the harmonic frequency. This process is known as heterodyning. Synchronous sampling techniques are better at separating the harmonic components, but require more expensive electronic hardware to perform the synchronous sampling and cannot be used simultaneously for broadband analysis. The use of tracking filters in a system for active control is described in U.S. Pat. No. 5,469,087 (Eatwell).
Neither system is very effective when multiple disturbance sources at different frequencies are present. In `Multi Axle Order Tracking with the Vold-Kalman Tracking filter`, H. Vold et al, Sound & Vibration Magazine, May 1997, pp30-34, a system for tracking multiple sources is described. This system estimates the complex envelopes of the signal components subject to the constraint that the envelopes can be represented locally by low-order polynomials. The resulting process is not well suited to implementation in `real-time`, and would result in considerable processing delay because of the nature of the constraints. This makes it unsuitable for application to real-time control systems. In addition, the process is numerically intensive. The measurement of disturbances experienced by rotating or reciprocating machinery often requires the use of multiple sensors. The data from these sensors is transmitted to a computer system for processing and analysis. The combination of multiple sensors and moderate frequency bandwidths will results in high data transfer rates. Considerable benefit would result if the data could be compressed before transmission or storage.
Characterization of Dynamic Response Model
System identification is the process of building a mathematical model of a dynamical system based on measurements of response of the system to known disturbances. This is usually done by applying the known disturbances to a mathematical model and then adjusting the parameters of the model until the output of the model is as close as possible to the measured output from the real system. This model is referred to as the system model or the dynamic response model.
System identification is a central part of modal analysis and control systems. In modal analysis, the dynamic response model of the system is parametrized by the frequency, damping and shape of a number of resonant modes. In order to conduct a modal analysis of a system it is usually necessary to cease the operation of the system. This means that modal analysis cannot be part of an on-line condition monitoring system.
System identification is also a central part of an adaptive control system, such as used for active noise and vibration control. In most control systems, a mathematical model of the physical system is assumed to be known from prior measurements or from numerical or analytical modelling. Once this information is known, the state of the system (usually current and prior conditions) can be estimated using known techniques. For example, if the statistics of the disturbance are known, an optimal `observer` may be used to estimate the current system state.
An example of a control system with on-line system identification is shown in FIG. 2. Test signal 4 is added at 75 to the output 74 of control system 114 to produce an actuator drive signal 76. The actuator 77 excites the dynamic system 1. The response of the dynamic system is measured by sensor 2 to produce sensor signal 3. The component of the sensor signal that is due to the test signal is estimated by passing the test signal 4 through adaptive filter 110 to produce an estimated response signal 111. This is subtracted from the sensor signal at 112 to give error signal 113, which is in turn used to adapt the coefficients of the filter 110. The control system 114 is responsive to the sensor signal 3 and, optionally, a reference signal 4. The system model is provided by the filter 110. Examples of such a control system are disclosed in U.S. Pat. No. 4,677,676 (Eriksson) and U.S. Pat. No. 5,553,153 (Eatwell).
Combined Systems
In some areas, such as system identification or modal testing, only the system model is required. In other areas, such as noise monitoring, only the characterization of the dynamic disturbance is required. However, in many areas, such as control of dynamical systems and condition-based monitoring of dynamical systems, both the dynamic disturbance and the system model are of interest and, moreover, they need to be measured at the same time.
For example, in many practical control systems the dynamic response of the physical system is time varying, in that the response to a given disturbance at one time will be different to the response to the same disturbance at a later time. In these cases it is necessary to continually re-estimate the dynamic response model whilst maintaining control of the system. One approach is described in chapter 7 of `Estimation and Control Interaction`, K. J. .ANG.stom and B. Wittenmark, Addison Wesley, 1989. The problem of Stochastic Adaptive Control is discussed, in which a hyperstate of system response parameters and signals is posed; i.e. the parameters are treated as slowly varying signals. No solutions to the problem are presented, except for an artificial example. One of the problems with this approach is that the signals usually vary much faster than the system parameters, so the problem will be ill-conditioned. Also, the processes discussed are not subject to external disturbances. In a disturbance control system, such as an active noise or vibration control system, the disturbance and the control signal will be highly correlated, so the control signal u and the process output y are not sufficient to characterize the system.
In prior disturbance control systems, the problems of system identification and control are addressed separately This results in an inefficient system which is subject to inaccuracies or slow operation.
In prior practical control systems, the estimation of the dynamic response is achieved by adding a low level test signal to the controller output and correlating this with the response at the system inputs. There are two major problems with this. Firstly, the level of the test signal must be kept low so that the control is not adversely affected, and secondly, as a consequence, the convergence rate of the estimation must be slow in order to decorrelate the test signal and the residual disturbance. This is a particular problem especially at start up when the disturbance may be large.
In on-line condition monitoring, the sound or vibration of a machine is monitored to determine if the machine is operating normally. Such a monitoring system infers information about the machine from the disturbance signals alone. In many machine failures the dynamic response of the system will also change prior to failure, so the monitoring could be improved significantly if the dynamic response could be measured. One of the main aims of condition-based maintenance is to avoid stopping the machine unnecessarily for checks, so it is usually not possible to stop the machine to perform a modal analysis or other system response measurement.
There is therefore a need for an analysis technique that can simultaneously characterize the a disturbance of a dynamical system and its dynamic response. There is also a need for an analysis technique that can simultaneously characterize the narrowband and broadband components of the disturbance, even when more than one narrowband source is present. There is also a need for an improved analysis system that can track rapid changes in disturbance and response parameters.
Objects
In view of the above limitations in the known art, an object of the current invention is to provide a method and apparatus for simultaneous characterization of the disturbance and the dynamic response model of a dynamical system.
A further object is to provide a method and apparatus for simultaneous characterization of narrowband and broadband components of the disturbance of a dynamical system.
A still further object of the invention is to provide a method and apparatus for estimating the disturbance parameters of a dynamical system and using them to provide a compressed representation of the disturbance.
A still further object of the invention is to provide a method and apparatus for controlling a dynamical system in which the control system simultaneously characterizes the disturbance and the dynamic response model of a dynamical system.